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Displaying 81 – 100 of 159

On the Brun-Titchmarsh theorem

James Maynard (2013)

Acta Arithmetica

The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(ϕ(q)logx) for some value C depending on logx/logq. Different authors have provided different estimates for C in different ranges for logx/logq, all of which give C>2 when logx/logq is bounded. We show that one can take C=2 provided that logx/logq ≥ 8 and q is sufficiently large. Moreover, we also produce a lower bound of size $x / (q^{1 / 2} ϕ (q))$ when logx/logq ≥ 8 and is bounded....

On the comparative theory of primes

Janos Pintz, Saverio Salerno (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the coprimality of certain multiplicative functions

E. Scourfield (1980)

Acta Arithmetica

On the distribution of the divisor function in arithmetic progressions

Yoichi Motohashi (1973)

Acta Arithmetica

On the exact number of primes in the arithmetic progression 4n ... 1 and 6n ... 1.

Alfred Brauer, Richard H. Hudson (1977)

Journal für die reine und angewandte Mathematik

On the greatest prime divisor of quadratic sequences

J. Pomykała (1991)

Journal de théorie des nombres de Bordeaux

On the greatest prime factor of a cubic polynomial.

Christopher Hooley (1978)

Journal für die reine und angewandte Mathematik

On the least prime in an arithmetic progression and estimates for the zeros of Dirichlet L-functions

Triantafyllos Xylouris (2011)

Acta Arithmetica

On the least prime in an arithmetic progression. I: The basic theorem

Ю.В. Линник (1944)

Matematiceskij sbornik

On the least prime in an arithmetic progression. II: The Deuring- Heilbronn theorem

Ю.В. Линник (1944)

Matematiceskij sbornik

On the moments of the Carmichael λ function

Florian Luca, Ayyadurai Sankaranarayanan (2006)

Acta Arithmetica

On the number of prime factors of a finite arithmetical progression

T. N. Shorey, R. Tijdeman (1992)

Acta Arithmetica

On the prime number theorem for the coefficients of certain modular forms

Alberto Perelli (1985)

Banach Center Publications

On the second moment for primes in an arithmetic progression

D. A. Goldston, C. Y. Yıldırım (2001)

Acta Arithmetica

On the Shanks-Rényi race problem

Jerzy Kaczorowski (1996)

Acta Arithmetica

On the size of the first factor of the class number of a cyclotomic field.

A. Granville (1990)

Inventiones mathematicae

On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus

Karin Halupczok (2009)

Journal de Théorie des Nombres de Bordeaux

For $ε > 0$ and any sufficiently large odd $n$ we show that for almost all $k \leq R : = n^{1 / 5 - ε}$ there exists a representation $n = p_{1} + p_{2} + p_{3}$ with primes $p_{i} \equiv b_{i}$ mod $k$ for almost all admissible triplets $b_{1}, b_{2}, b_{3}$ of reduced residues mod $k$ .

On Zeros of Dirirchlet's L Series.

H. Iwaniec (1974)

Inventiones mathematicae

Pretentiousness in analytic number theory

Andrew Granville (2009)

Journal de Théorie des Nombres de Bordeaux

In this report, prepared specially for the program of the XXVième Journées Arithmétiques, we describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of “pretentiousness” to help us better understand several key questions in analytic number theory.

Prime constellations in triangles with binomial coefficient congruences

Larry Ericksen (2009)

Acta Mathematica Universitatis Ostraviensis

The primality of numbers, or of a number constellation, will be determined from residue solutions in the simultaneous congruence equations for binomial coefficients found in Pascal’s triangle. A prime constellation is a set of integers containing all prime numbers. By analyzing these congruences, we can verify the primality of any number. We present different arrangements of binomial coefficient elements for Pascal’s triangle, such as by the row shift method of Mann and Shanks and especially by...

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